1. Stating the problem: We have four equations involving $n$: 1) $65 + 35 = n$ 2) $n + 65 = 35$ 3) $65 - n = 35$ 4) $n - 35 = 65$ 2. Solve each equation step-by-step. 3. For equation 1: $65 + 35 = n$ Calculate the sum: $$n = 65 + 35 = 100$$ 4. For equation 2: $n + 65 = 35$ Subtract 65 from both sides: $$n + 65 - \cancel{65} = 35 - \cancel{65}$$ $$n = -30$$ 5. For equation 3: $65 - n = 35$ Subtract 65 from both sides: $$65 - n - 65 = 35 - 65$$ $$-n = -30$$ Multiply both sides by $-1$: $$n = 30$$ 6. For equation 4: $n - 35 = 65$ Add 35 to both sides: $$n - 35 + \cancel{35} = 65 + \cancel{35}$$ $$n = 100$$ Final answers: - Equation 1: $n = 100$ - Equation 2: $n = -30$ - Equation 3: $n = 30$ - Equation 4: $n = 100$